Keisha's boat has a top speed of 9 miles per hour in still water. while traveling on a river at top speed, she went 10 miles upstream in the same amount of time she went 20 miles downstream. find the rate of the river current.

If she went 10 miles upstream in the same time as she went 20 miles downstream, that means the downstream speed is twice the upstream speed.

The speed is still water is 9 mph.
The speed of the current is c.
Going downstream, the current adds speed, so the sped downstream is 9 + c.
The speed upstream is 9 - c.
9 + c is twice 9 - c.

9 + c = 2(9 - c)

9 + c = 18 - 2c

3c = 9

c = 3

The speed of the current is 3 mph.

Check:
9 + c = 12
9 - c = 6
By taking into the account the speed of the current, the downstream speed, 12 mph, is indeed twice the upstream sped, 6 mph.